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On financial applications of the two-parameter Poisson-Dirichlet distribution

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  • Sergey Sosnovskiy

Abstract

Capital distribution curve is defined as log-log plot of normalized stock capitalizations ranked in descending order. The curve displays remarkable stability over periods of time. Theory of exchangeable distributions on set partitions, developed for purposes of mathematical genetics and recently applied in non-parametric Bayesian statistics, provides probabilistic-combinatorial approach for analysis and modeling of the capital distribution curve. Framework of the two-parameter Poisson-Dirichlet distribution contains rich set of methods and tools, including infinite-dimensional diffusion process. The purpose of this note is to introduce framework of exchangeable distributions on partitions in the financial context. In particular, it is shown that averaged samples from the Poisson-Dirichlet distribution provide approximation to the capital distribution curves in equity markets. This suggests that the two-parameter model can be employed for modelling evolution of market weights and prices fluctuating in stochastic equilibrium.

Suggested Citation

  • Sergey Sosnovskiy, 2015. "On financial applications of the two-parameter Poisson-Dirichlet distribution," Papers 1501.01954, arXiv.org, revised Jul 2015.
    • Handle: RePEc:arx:papers:1501.01954
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    References listed on IDEAS

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    1. Masanao Aoki, 2003. "Applications of Exchangeable Random Partitions to Economic Modeling," UCLA Economics Online Papers 228, UCLA Department of Economics.
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    3. Garibaldi,Ubaldo & Scalas,Enrico, 2010. "Finitary Probabilistic Methods in Econophysics," Cambridge Books, Cambridge University Press, number 9780521515597.
    4. U. Garibaldi & D. Costantini & P. Viarengo, 2007. "The two-parameter Ewens distribution: a finitary approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 2(2), pages 147-161, December.
    5. Robert Fernholz & Tomoyuki Ichiba & Ioannis Karatzas, 2013. "A second-order stock market model," Papers 1302.3870, arXiv.org.
    6. Masanao Aoki, 2001. "Modeling Aggregate Behavior and Fluctuations in Economics: Stochastic Views of Interacting Agents," UCLA Economics Online Papers 142, UCLA Department of Economics.
    7. Aoki,Masanao, 2004. "Modeling Aggregate Behavior and Fluctuations in Economics," Cambridge Books, Cambridge University Press, number 9780521606196.
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    Cited by:

    1. Dassios, Angelos & Zhang, Junyi, 2021. "Exact simulation of two-parameter Poisson-Dirichlet random variables," LSE Research Online Documents on Economics 107937, London School of Economics and Political Science, LSE Library.
    2. Eric Andr'e & Guillaume Coqueret, 2020. "Dirichlet policies for reinforced factor portfolios," Papers 2011.05381, arXiv.org, revised Jun 2021.

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